Solving a Uniform Motion Application: Biking Speed with Equal Travel Times
Apply the distance, rate, and time problem-solving strategy to find an unknown vehicle speed when different distances are covered in equal time—one segment with a headwind and one with a tailwind.
Problem: Link has an electric bike which runs at a constant speed. He can ride his bike miles into a mph headwind in the same amount of time he can ride miles with a mph tailwind. What is Link’s biking speed?
- Read and draw: Sketch two paths — one for miles against the wind and one for miles with the wind. Create a rate–time–distance table.
- Identify: Link's biking speed in still air.
- Name: Let = Link's biking speed. The headwind rate is ; the tailwind rate is . Because , the times are and .
- Translate: The travel times are equal:
- Solve: Multiply both sides by the LCD, :
- Check: Headwind time: hours. Tailwind time: hours. The times are equal.
- Answer: Link's biking speed is mph.
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Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax
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